verde.median_distance

verde.median_distance(coordinates, k_nearest=1, projection=None)

Median distance between the k nearest neighbors of each point.

For each point specified in coordinates, calculate the median of the distance to its k_nearest neighbors among the other points in the dataset. Sparse uniformly spaced datasets can use k_nearest of 1. Datasets with points clustered into tight groups (e.g., densely sampled along a flight line or ship treck) will have very small distances to the closest neighbors, which is not representative of the actual median spacing because it doesn’t take the spacing between lines into account. In these cases, a median of the 10 or 20 nearest neighbors might be more representative.

The distances calculated are Cartesian (l2-norms) and horizontal (only the first two coordinate arrays are used). If the coordinates are in geodetic latitude and longitude, provide a projection function to convert them to Cartesian before doing the computations.

Note

If installed, package pykdtree will be used instead of scipy.spatial.cKDTree for better performance.

Parameters

• coordinates (tuple of arrays) – Arrays with the coordinates of each data point. Should be in the following order: (easting, northing, vertical, …). Only the first two coordinates (assumed to be the horizontal) will be used in the distance computations.

• k_nearest (int) – Will calculate the median of the k nearest neighbors of each point. A value of 1 will result in the distance to nearest neighbor of each data point.

• projection (callable or None) – If not None, then should be a callable object (like a function) projection(easting, northing) -> (proj_easting, proj_northing) that takes in easting and northing coordinate arrays and returns projected northing and easting coordinate arrays.

Returns

distances (array) – An array with the median distances to the k nearest neighbors of each data point. The array will have the same shape as the input coordinate arrays.

Examples

>>> import verde as vd
>>> import numpy as np
>>> coords = vd.grid_coordinates((5, 10, -20, -17), spacing=1)
>>> # The nearest neighbor distance should be the grid spacing
>>> distance = median_distance(coords, k_nearest=1)
>>> np.allclose(distance, 1)
True
>>> # The distance has the same shape as the coordinate arrays
>>> print(distance.shape, coords[0].shape)
(4, 6) (4, 6)
>>> # The 2 nearest points should also all be at a distance of 1
>>> distance = median_distance(coords, k_nearest=2)
>>> np.allclose(distance, 1)
True
>>> # The 3 nearest points are at a distance of 1 but on the corners they
>>> # are [1, 1, sqrt(2)] away. The median for these points is also 1.
>>> distance = median_distance(coords, k_nearest=3)
>>> np.allclose(distance, 1)
True
>>> # The 4 nearest points are at a distance of 1 but on the corners they
>>> # are [1, 1, sqrt(2), 2] away.
>>> distance = median_distance(coords, k_nearest=4)
>>> print("{:.2f}".format(np.median([1, 1, np.sqrt(2), 2])))
1.21
>>> for line in distance:
...     print(" ".join(["{:.2f}".format(i) for i in line]))
1.21 1.00 1.00 1.00 1.00 1.21
1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00 1.00 1.00 1.00 1.00
1.21 1.00 1.00 1.00 1.00 1.21